Naturally, this forms the starting point for more direct applications of noncommutative geometry to particle physics phenomenology. Instead of the spectral action playing the role of a bare action functional, to which subsequent RG-methods are applied, we now have a candidate for a so-called quantum effective spectral action, given by the sum of all 1PI Feynman diagrams and which is supposed to be valid at all energies.
One may then try to extend the derivation of bare physical Lagrangians from the spectral action [1]}, [2]} to the renormalized spectral action, and arrive at a spectral, noncommutative geometric description of particle physics which is also valid and falsifiable at lower energies.
